There are many problems whose solution requires proof that a quadrilateral is cyclic. The main reason for writing this paper is to offer a number of new tools for proving that a particular quadrilateral is cyclic, thus expanding the present knowledge base and ensuring that investigators in mathematics and teachers of mathematics have at their disposal the most suitable tool available for solving the problem at hand. This present paper presents an overall summary and further development (accompanied by proofs) of the geometrical properties associated with cyclic quadrilaterals. Some of the properties are well known, others are less known, some are surprising and some are, to the best of our knowledge, heretofore unknown.